REPLY Reply to the discussion by Markiewicz et al. Juraj M. Cunderlik a, * , Donald H. Burn b a Conestoga-Rovers and Associates, 651 Colby Drive, Waterloo, Ont., Canada N2V 1C2 b Department of Civil Engineering, University of Waterloo, Waterloo, Ont., Canada N2L 3G1 Received 7 March 2006; accepted 17 April 2006 We are pleased to learn that our method of non-stationary pooled flood frequency analysis (method, hereafter), which was published in the Journal of Hydrology in 2003 (Cunderlik and Burn, 2003), still attracts the interest of readers of this journal. The discussion of Markiewicz et al. (2006) on this method provides us with the opportunity to explain certain aspects of the methodology in greater detail. Markiewicz et al. (2006) in their original discussion try to convey their understanding of the method and compare it to their approach of local non-stationary flood frequency anal- ysis (Strupczewski et al., 2001; Strupczewski and Kacz- marek, 2001), which they refer to as the ‘‘conventional’’ approach. Since we believe there has not yet been a con- ventional approach established in this emerging field of hydrology, we will refer in the following text to this ap- proach as Strupczewski’s approach. First, let us re-state the main objective of our method. As the title of the paper suggests, the objective was to develop a new approach for non-stationary pooled flood frequency analysis (PFFA). The main novelty of the method is the combination of PFFA with a robust trend estimation technique. The method provides a methodology for assess- ing the statistical significance of non-stationarity in the first two linear moments of the series at both local and regional scales. The non-stationary pooled quantile function is sepa- rated into a local time dependent component and a regional component that is regarded as time-invariant, under the assumption of second-order non-stationarity. In contrast to other approaches (including Strupczewski’s approach), the method takes advantage of the L-moments approach (e.g., linearity, existence) (Hosking and Wallis, 1997) in the time-dependent quantile estimation. Perhaps the first major misinterpretation of the method by Markiewicz et al. (2006) is that the trend in the mean deviation Eq. (9) is used to estimate the trend in the stan- dard deviation (r). As a matter of fact, the non-stationary scale parameter is represented by the second linear mo- ment, which is, in the case of a standardized Qmax series, the coefficient of linear variation (Cunderlik and Burn, 2003, p. 215). This hopefully explains the estimation of trend magnitudes in the first two linear moments of a non-stationary series. Another misunderstanding of Markiewicz et al. (2006) is related to the selection of Sen’s method and to the adjust- ment of regression coefficients. Sen’s estimator (Sen, 1968) is a non-parametric alternative for estimating a slope. In contrast to the LS method, Sen’s method is insensitive to extreme outliers, and can handle missing values (Hirsh et al., 1982). The adjustment of regression coefficients is applied to account for sampling variability, as explained in Figs. 5 and 6. The last important comment refers to the stationariza- tion of the Qmax series and the dimension of Q(t), l i (t), and r i (t) in Eq. (17). As already stated above, and in the ori- ginal text (Cunderlik and Burn, 2003, p. 212), the Qmax ser- ies, following the philosophy of the index flood method, is standardized prior to the stationarization. Hence, the aver- age residual component is equal to zero. Finally, since the series is standardized, only l i has units of Q(t). 0022-1694/$ - see front matter  c 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2006.04.028 * Corresponding author. Tel.: +1 519 884 0510; fax: +1 519 884 5256. E-mail address: jcunderlik@craworld.com (J.M. Cunderlik). Journal of Hydrology (2006) 331, 367– 368 available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/jhydrol